Appendix C Transmission Dynamics of Coexisting Chlamydial and HIV Infections in the United States

Introduction

Predicting HIV prevalence and incidence trends in the United States is hazardous because the mechanisms of heterosexual HIV transmission, the interrelationships between classical STDs and HIV infection, and sexual behavior among the U.S. population are not fully understood. These factors are particularly important when determining the rate of spread of HIV in different risk groups and the potential impact of STDs on heterosexual HIV transmission. Nevertheless, mathematical models of disease transmission can be used to investigate whether HIV, once introduced in the general heterosexual population, is able to establish and persist solely by heterosexual transmission, without the contribution of high-risk groups such as intravenous drug users or bisexuals. If so, how fast will HIV spread and to what extent will new HIV infections be attributable to curable STDs? A deterministic mathematical model has been developed to represent the natural course of STD and HIV infection in the general, sexually active, heterosexual population of the United States. Chlamydial infection is specifically modeled because it affects a large proportion of individuals not usually at risk for STDs and could therefore play an important role in heterosexually transmitted HIV infections, not only from high-risk to low-risk groups but also within low-risk groups. Results of the model will be discussed in relation to all curable STDs.

1

Centre de Recherche Hôpital du St-Sacrément and Département de Médecine Sociale et Préventive, Université Laval (Center for Research, Hospital of St. Sacrement and Department of Social and Preventive Medicine, University of Laval, Quebec City, Canada).

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Appendix C Transmission Dynamics of Coexisting Chlamydial and HIV Infections in the United States
Marie-Claude Boily1
Introduction
Predicting HIV prevalence and incidence trends in the United States is hazardous because the mechanisms of heterosexual HIV transmission, the interrelationships between classical STDs and HIV infection, and sexual behavior among the U.S. population are not fully understood. These factors are particularly important when determining the rate of spread of HIV in different risk groups and the potential impact of STDs on heterosexual HIV transmission. Nevertheless, mathematical models of disease transmission can be used to investigate whether HIV, once introduced in the general heterosexual population, is able to establish and persist solely by heterosexual transmission, without the contribution of high-risk groups such as intravenous drug users or bisexuals. If so, how fast will HIV spread and to what extent will new HIV infections be attributable to curable STDs? A deterministic mathematical model has been developed to represent the natural course of STD and HIV infection in the general, sexually active, heterosexual population of the United States. Chlamydial infection is specifically modeled because it affects a large proportion of individuals not usually at risk for STDs and could therefore play an important role in heterosexually transmitted HIV infections, not only from high-risk to low-risk groups but also within low-risk groups. Results of the model will be discussed in relation to all curable STDs.
1
Centre de Recherche Hôpital du St-Sacrément and Département de Médecine Sociale et Préventive, Université Laval (Center for Research, Hospital of St. Sacrement and Department of Social and Preventive Medicine, University of Laval, Quebec City, Canada).

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Model And Parameter Assumptions
The deterministic mathematical model used, which is compartmental in structure, describes dynamically the course of both chlamydial and HIV infections in an active heterosexual population stratified by sex and sexual activity. The different stages of HIV and chlamydial infections are represented by six compartments. In the model, an individual can be susceptible to HIV, be infected with HIV but asymptomatic, or have full-blown AIDS. Each of these groups could be infected with an STD or not. Individuals can pass from one disease state to another at different rates, depending on the demographic and behavioral characteristics of the population as well as the natural history of the STD and HIV infections. The details of the model, including information on the system of nonlinear differential equations describing changes in the size of the population with time for the different disease states, are described by Boily and others (in press) in an upcoming paper.
The numerical studies of the model are based upon an initial population size of 171,481,800 individuals corresponding to the general, sexually active, heterosexual population of the United States in 1995 (Leigh et al., 1993; CIA, 1995; U.S. Census Bureau, 1996). The population growth rate is assumed to be 1.1 percent in absence of HIV infection, with a 1.01:1.00 female-to-male ratio (CIA, 1995; U.S. Census Bureau, 1996). It is assumed that an individual remains sexually active for a period of 55 years from age 15 to 70 (Anderson and Dahlberg, 1992; Leigh et al., 1993; Seidman and Rieder, 1994). Each gender is divided into six sexual activity classes to represent people with different rates of partner acquisition.
The most important assumptions when evaluating the potential impact of STDs on heterosexual HIV transmission center around HIV transmission probabilities in the absence of STDs, the sexual network and the distribution of sexual activity in the general population, the prevalence of STDs, and the nature and the magnitude of the interrelationships between STDs and HIV infection. These parameters determine whether HIV, in the presence or absence of STDs, can establish in the population and what the rate of spread of HIV in different risk groups will be. In the absence of the enhancing STD, the male-to-female per partner transmission probability for HIV is assumed to be two times that of female-to-male transmission (European Study Group on Heterosexual Transmission of HIV, 1992; Garnett and Anderson, 1993b; de Vincenzi and European Study Group on Heterosexual Transmission of HIV, 1994; Mastro et al., 1994;). In addition, HIV transmission probabilities are reduced when partnerships are formed with individuals from the high-activity classes (Jewell and Shiboski, 1990; Brookmeyer and Gail, 1994; Downs and de Vincenzi, 1996) to reflect the fact that very active individuals perform fewer acts per partnership than those with fewer partners (Garnett and Anderson, 1995; Boily and Anderson, 1996; Boily et al., in press). Lastly, different mechanisms have been postulated about

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the way STDs interact with HIV infection (Pepin et al., 1989; Piot and Tezzo, 1990; Laga et al., 1991, 1993; Wasserheit, 1992; Wald et al., 1993; Laga, Diallo, et al., 1994; Grosskurth et al., 1995).
The interrelationship between HIV infection and chlamydial infection is defined strictly as an increase in HIV transmission probability (the relative risk) due to increased HIV susceptibility and infectivity in presence of the cofactor chlamydial (May and Anderson, 1989; Boily and Anderson, 1996). To account for the variability in the estimates from different studies (Plummer et al., 1991; Wasserheit, 1992; Laga et al., 1993; Wald et al., 1993), it was assumed that chlamydial increases HIV transmission probability by 3.6- and 5-fold. In this model, the epidemic is seeded by introducing one HIV infected person in the female activity class 6 in 1980. The annual rates of new partner acquisition of the six sexual activity classes for the model (Table C-1) were derived from different national sex surveys of the general population (Anderson and Dahlberg, 1992; Leigh et al., 1993; Laumann et al., 1994; Seidman and Rieder, 1994) that report approximately 10 percent of the general population had more than two partners in the previous year (Table C-2). The problems with such data, as with most data on sexual behavior in the general population (ACSF Investigators, 1992; Anderson and Dahlberg, 1992; Johnson et al., 1992; Leigh et al., 1993; Seidman and Reider, 1994; Laumann et al., 1994; Turner et al., 1995), are that for a variety of reasons (Morris, 1993; Wadsworth et al., 1996), men usually report more female partners than females do male partners. This is inconsistent with the fact that men and women are having sex with each other (Blower and McLean, 1991; Boily and Anderson, 1991; Morris, 1993; Wadsworth et al., 1996). Thus, for simplicity and to ensure that the mean number of sex partners between the male and female population is balanced (Blower and McLean, 1991; Boily and Anderson, 1991; Lepont and Blower, 1991), we assumed that males and females have a similar distribution in sexual activity. The simulations have been performed under an assortative mixing scenario (Garnett and Anderson, 1993b; Garnett et al., 1996) or, in other words, one where the individual prefers to choose his or her partners within the same activity class (a minimum of 44 percent of partner formation occurs within members of the same activity class). The fact that, under proportionate mixing (individuals choose their sexual partners at random, depending on availability only) (Haralosottir et al., 1992; Boily and Brunham, 1993), chlamydial and HIV infections cannot establish in the population even with a relative risk of 5 further supports this hypothesis.
The predicted HIV and AIDS trends and estimates of the fraction of cases attributable to cofactor chlamydial were produced using different sets of realistic parameter assumptions in which HIV transmission probabilities were varied depending on the magnitude of association used. The various biological and demographic parameter values used for chlamydial and HIV infection are summarized in Table C-3, and those on sexual behavior and initial chlamydial prevalence are

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the general population (both sexes and all sexual activity classes), (b) the low-risk group (annual rate of partner change less than one per year), and (c) the high-risk group (annual rate of partner change greater than one per year) in Figure C-1. Fast and slow spread scenarios are represented. Both are based on the parameters described in Table C-3 with a relative risk of 5 except that, for the slow scenario, HIV transmission probabilities are reduced by 25 percent.
HIV trends predicted by the model suggest that the establishment of HIV in the heterosexual population is possible and may affect a considerable proportion of the general population and different risk groups. The rate at which HIV will propagate and the maximum fraction of the population afflicted by HIV infection are highly dependent on the degree to which chlamydial infection enhances HIV transmission and on the prevalence of chlamydial infection. At the time of introduction of HIV in the population in 1980, chlamydial infection affected 0.72 percent and 0.68 percent of the general female and male population (weighted average of the different activity classes), but rates were higher in the most sexually active individuals (Table C-1), thus emphasizing their contribution to HIV transmission. Under the set of conditions investigated, HIV infection cannot establish in the absence of chlamydial infection, without a minimum degree of within-group mixing between high-activity classes or in the absence of the highest-activity class (class 6). Under the latter two conditions, chlamydial infection cannot persist either. Thus, a large fraction of HIV infections will, even over a short time period, be attributable to the cofactor chlamydial and the core group population.
The predicted fraction of the total incident heterosexual HIV and AIDS cases attributable to chlamydial infection for the periods 1980-1994 inclusive, 1995-1999, and 1995-2004 are presented in Table C-4 for the slow and fast scenarios with a relative risk of 3.6 and 5.
For all scenarios investigated, a large fraction of HIV infections can, even over a short time period, be attributed to cofactor chlamydial. For example, the model predicts that during 1990-1994, more than 86 percent and 95 percent of the heterosexual AIDS and HIV cases, respectively, could have been prevented by treating chlamydial infections.
Discussion
Despite limitations of the model due to major uncertainties concerning parameter assumptions, mathematical modeling can be used to evaluate the magnitude of the HIV/AIDS epidemic and the role of STDs in heterosexual HIV transmission. The real impact of STDs on the pattern of HIV incidence and prevalence in the United States remains uncertain because it mainly depends on the prevalence of STDs in different risk groups, the interrelationships between STD and HIV infection, the real magnitude of association, and the estimates of HIV transmission

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FIGURE C-1 Predicted prevalence and incidence trends of HIV infection, 1980 to 2005, in the sexually active U.S. heterosexual population. Graph A represents the general population (both sexes and all sexual activity classes), with initial prevalence of chlamydial infection = 0.70 percent; Graph B depicts the low-risk group (annual rate of partner change less than one per year), with initial prevalence of chlamydial infection = 0.01 percent; and Graph C represents the high-risk group (annual rate of partner change greater than one per year), with initial prevalence of chlamydial infection = 4.63 percent. Fast and slow spread scenarios also are represented. Both are based on the parameters described in Table C-3 with a relative risk of 5 except that, for the slow scenario, HIV transmission probabilities are reduced by 25 percent.

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probability in the absence of STDs. Additional data are needed for all these factors.
From the different scenarios considered, there are a variety of reasons to conclude that a self-sustaining HIV epidemic in the general heterosexual population is possible. First, the behavioral parameter values used underestimate the variability in sexual activity of the general population because the most sexually active individuals, who constitute a small fraction of the population, are most probably undersampled in a random sample of the general population. Greater heterogeneity in sexual activity and higher activity levels of the most active individuals are conditions that favor the establishment of an STD. Second, previous results (Garnett et al., 1992; Whitaker and Renton, 1992; Garnett and Anderson, 1993a; Boily et al., in press) show that a more assortative mixing or a majority of individuals having a low rate of partner change accentuate partner formation between high-activity classes. Thus, even with a lower level of sexual activity, a more assortative mixing would favor STD establishment and transmission. Third, chlamydial infection prevalence rates produced in the different risk groups before the introduction of HIV are lower than the rates currently reported (prevalence of chlamydial infection in young adult women and sexually active adolescents greater than 5 percent and 10 percent, men from STD clinics up to 15 to 20 percent, young asymptomatic men seen in more general medical settings greater than 3 to 5 percent). Fourth, by considering the general heterosexual population exclusively, the model does not account for the fact that many heterosexual contacts and transmissions occur with high-risk individuals such as intravenous drug users and bisexuals, for whom HIV and STD rates are higher. Fifth, if a causal relationship exists between chlamydial and HIV infections, then the magnitude of association is very likely to be underestimated (Hayes et al., 1995; Boily and Anderson, 1996). Thus, the real increase in HIV transmission probabilities per partnership or per contact due to the cofactor chlamydial could be higher than what has been reported, a relative risk of 3.6, in the best study (Laga, Alary, et al., 1994).
Two elements that have the potential to modify the global picture of HIV spread and that were not included in the model are spatial heterogeneity and the heterogeneity in HIV transmission probabilities during the long incubation period. It was assumed that the U.S. population was homogeneously distributed geographically. This implies that the rate of spread of HIV predicted may be faster than in reality, as HIV might be introduced at different times in different agglomerations. Thus, on the one hand, spatial heterogeneity could retard diffusion of HIV from one agglomeration to another and display great variability in the rate of spread between regions or districts, but it should not compromise the reproductive success of HIV infection, which was shown to be viable in a spatially homogeneous population. On the other hand, if heterogeneity in HIV transmission probabilities (with high transmission probabilities in the first and last phase of the incubation period) were included in the model, then, in its initial

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phase, the epidemic could develop at a faster rate than predicted by the model (Blythe and Anderson, 1988).
Given a fixed trend, the effect of STD treatment on future HIV trends and the maximum proportion of HIV infections prevented are highly dependent on the degree to which STDs enhance HIV transmission, on the prevalence of STDs, and on the combination between the pattern of sexual behavior in the general population and the estimates of HIV transmission probability in the absence of STDs. The strongest assumption of this analysis is the extent to which HIV spread depends on chlamydial, since HIV cannot establish in the absence of enhancing chlamydial. This assumption is not totally unrealistic if we consider (despite other dissimilarities) that in many Northern European countries, where STDs are better controlled compared to the United States, there is little evidence of an indigenous heterosexual HIV epidemic (King K. Holmes, University of Washington, personal communication, August 1996). Thus, the model and parameters used may portray an overly optimistic scenario of the impact of chlamydial treatment on HIV incidence trends, because the model suggests that heterosexually transmitted HIV could in theory be eradicated if chlamydial were eliminated. Note that even if HIV could establish in the absence of chlamydial, a considerable fraction of HIV cases could still be attributed to cofactor chlamydial. HIV spread would slow down, but would not be eradicated by effective STD treatment alone. In addition, in the United States, the continued force of heterosexual transmission from intravenous drug use would remain. Note also that even if chlamydial infection accounts for a large fraction of new HIV cases in this model, this does not preclude the possibility that other STDs have also contributed to the spread of HIV once it has become established. The model with chlamydial is equivalent to assuming that all STDs are required for HIV to establish. Under this assumption, the eradication of heterosexually transmitted HIV is possible by eliminating only one curable STD or by reducing the prevalence of all curable STDs below a certain threshold. Another way the same HIV epidemic could be established is by assuming that it requires the presence of only one STD, such as chlamydial. This scenario is more conservative regarding the impact of STD treatment on HIV incidence trends, since the elimination of HIV would require the eradication of all STDs or the reduction of the prevalence of all curable STDs below a threshold much lower that that for the first scenario.
Despite the depressing forecast of the model on the potential impact of chlamydial infection and other STDs on HIV spread in the general U.S. heterosexual population, one optimistic point emerges from this study. This is the important fraction of heterosexually transmitted HIV infections that can be prevented by treating chlamydial infection and other curable STDs. Simulation work confirms previous results (Hethcote and Yorke, 1984) showing that screening high-risk individuals or core groups can be much more efficient than the screening of the more general population (Hethcote and Yorke, 1984; Brunham and

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Plummer, 1990; Garnett and Anderson, 1995), because the noncore population contributes relatively little to the reproductive success of STDs and HIV infection. Thus, a 50 percent reduction in chlamydial (from 10 to 5 percent), such as observed in Region X of the United States (DeLisle et al., 1993) following the implementation of a chlamydial screening program in family planning clinics, could play an important role in slowing HIV transmission in the area. Moreover, treating STDs offers a complementary approach to interventions to change sexual behavior (such as reduction of sexual activity). Furthermore, changes in sexual behavior can produce pernicious effects by modifying the structure of social networks (Boily and Anderson, 1990; Thompson Fullilove, 1995).
Considering the great heterogeneity in seroprevalence rates of infection between regions (CDC, 1994, 1995), it can be assumed that the HIV epidemic in the heterosexual population in most U.S. states and cities might still be in its early stages (i.e., anywhere between 1980 and 2000 on our time scale). Results indicate that improved efforts to contain and prevent STDs should be made immediately and that such efforts could prevent, if initiated early enough, many new HIV infections, even over a relatively short time period. However, since exposure of the general heterosexual population to HIV via high-risk individuals such as intravenous drug users or bisexuals has not been included in the model (deliberately done in order to remain conservative), one should bear in mind that constant introduction of the virus in the general heterosexual population by these high-risk groups can always occur despite excellent STD control. Therefore, it is important when designing prevention strategies for the general heterosexual population not to ignore these remaining reservoirs of STDs, including HIV infection.
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Boily M-C, Anderson RM. Assessing change in sexual behavior using mathematical models: the impact of sexual mixing (Part A). Proceedings of the International Conference on Assessing AIDS Prevention, October 29-November 1, 1990; Montreux, Switzerland [abstract no. C2.4].
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